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International Conference on Automated Deduction

CADE 2015: Automated Deduction - CADE-25 pp 152–162Cite as

Encoding Dependency Pair Techniques and Control Strategies for Maximal Completion

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9195))

Abstract

This paper describes two advancements of SAT-based Knuth-Bendix completion as implemented in Maxcomp. (1) Termination techniques using the dependency pair framework are encoded as satisfiability problems, including dependency graph and reduction pair processors. (2) Instead of relying on pure maximal completion, different SAT-encoded control strategies are exploited.

Experiments show that these developments let Maxcomp improve over other automatic completion tools, and produce novel complete systems.

This research was supported by the Austrian Science Fund project I963.

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References

  1. Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)

    Google Scholar 

  2. Dutertre, B., de Moura, L.: A fast linear-arithmetic solver for DPLL(T). In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 81–94. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  3. Endrullis, J., Waldmann, J., Zantema, H.: Matrix interpretations for proving termination of term rewriting. JAR 40(2–3), 195–220 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Giesl, J., Thiemann, R., Schneider-Kamp, P.: The dependency pair framework: combining techniques for automated termination proofs. In: Baader, F., Voronkov, A. (eds.) LPAR 2004. LNCS (LNAI), vol. 3452, pp. 301–331. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  5. Klein, D., Hirokawa, N.: Maximal completion. In: RTA, vol. 10 of LIPIcs, pp. 71–80 (2011)

    Google Scholar 

  6. Korovin, K.: Inst-Gen – a modular approach to instantiation-based automated reasoning. In: Voronkov, A., Weidenbach, C. (eds.) Programming Logics. LNCS, vol. 7797, pp. 239–270. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  7. Sato, H., Winkler, S.: A satisfiability encoding of dependency pair techniques for maximal completion. In: WST (2014)

    Google Scholar 

  8. Schneider-Kamp, P., Thiemann, R., Annov, E., Codish, M., Giesl, J.: Proving termination using recursive path orders and SAT solving. In: Konev, B., Wolter, F. (eds.) FroCos 2007. LNCS (LNAI), vol. 4720, pp. 267–282. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  9. Sternagel, T., Zankl, H.: KBCV – Knuth-Bendix Completion Visualizer. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS, vol. 7364, pp. 530–536. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  10. Stump, A., Löchner, B.: Knuth-Bendix completion of theories of commuting group endomorphisms. IPL 98(5), 195–198 (2006)

    Article  MATH  Google Scholar 

  11. Wehrman, I., Stump, A., Westbrook, E.: Slothrop: knuth-bendix completion with a modern termination checker. In: Pfenning, F. (ed.) RTA 2006. LNCS, vol. 4098, pp. 287–296. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  12. Winkler, S., Sato, H., Middeldorp, A., Kurihara, M.: Multi-completion with termination tools. JAR 50(3), 317–354 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  13. Yamada, A., Kusakari, K., Sakabe, T.: A unified ordering for termination proving. Science of Computer Programming (2014). doi:10.1016/j.scico.2014.07.009

  14. Zankl, H., Hirokawa, N., Middeldorp, A.: Constraints for argument filterings. In: van Leeuwen, J., Italiano, G.F., van der Hoek, W., Meinel, C., Sack, H., Plášil, F. (eds.) SOFSEM 2007. LNCS, vol. 4362, pp. 579–590. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  15. Zankl, H., Hirokawa, N., Middeldorp, A.: KBO orientability. JAR 43(2), 173–201 (2009)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Graduate School of Information Science and Technology, Hokkaido University, Sapporo, Japan

    Haruhiko Sato

  2. Institute of Computer Science, University of Innsbruck, Innsbruck, Austria

    Sarah Winkler

Authors
  1. Haruhiko Sato
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  2. Sarah Winkler
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Corresponding author

Correspondence to Haruhiko Sato .

Editor information

Editors and Affiliations

  1. University of Ottawa, Ottawa, Canada

    Amy P. Felty

  2. University of Innsbruck, Innsbruck, Austria

    Aart Middeldorp

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Sato, H., Winkler, S. (2015). Encoding Dependency Pair Techniques and Control Strategies for Maximal Completion. In: Felty, A., Middeldorp, A. (eds) Automated Deduction - CADE-25. CADE 2015. Lecture Notes in Computer Science(), vol 9195. Springer, Cham. https://doi.org/10.1007/978-3-319-21401-6_10

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  • DOI: https://doi.org/10.1007/978-3-319-21401-6_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21400-9

  • Online ISBN: 978-3-319-21401-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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